heating old neutron stars andreas reisenegger pontificia universidad católica de chile (uc) with...
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Heating old neutron stars
Andreas ReiseneggerPontificia Universidad Católica de Chile (UC)
with
Rodrigo Fernández
formerly UC undergrad., now PhD student @ U. of Toronto
Paula Jofré
formerly UC undergrad., admitted to
International Max Planck Research School, Garching
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Heating neutron star matter by weak interactions
• Chemical (“beta”) equilibrium sets relative number densities of particles (n, p, e, ...) at different pressures
• Compressing or expanding a fluid element perturbs equilibrium
• Non-equilibrium reactions tend to restore equilibrium
• “Chemical” energy released as neutrinos & “heat”
epnepn ),(
epn e.g.,
eepn
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Possible forcing mechanisms
• Neutron star oscillations (bulk viscosity): SGR flare oscillations, r-modes – Not promising
• Accretion: effect overwhelmed by external & crustal heat release – No.
• d/dt: “Rotochemical heating” – Yes
• dG/dt: “Gravitochemical heating” - !!!???
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“Rotochemical heating”
NS spin-down (decreasing centrifugal support) progressive density increase chemical imbalance non-equilibrium reactions internal heating possibly detectable thermal emission
Reisenegger 1995, 1997; Fernández & Reisenegger 2005; Reisenegger et al. 2006, submitted (all ApJ)
0, epn
,),( eepn
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Fast vs. slow processes
“Direct Urca”
FastBut not allowed if proton
density too low.
“Modified Urca”
Dominant process if direct Urca not allowed, but:
Much slower
epnnn epn
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Yakovlev & Pethick 2004
Standard neutron star cooling:
1) No thermal emission after 10 Myr.
2) Cooling of young neutron stars in (very) rough agreement with slow cooling models. (?)
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Thermo-chemical evolution
,:radiation
throughdecrease
epn
throughincrease
dt
dT
epn
throughdecrease
ncompressio
throughincrease
dt
d
Variables:•Chemical imbalances•Internal temperature TBoth are uniform in diffusive equilibrium.
μe,pnμe, μμμη
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MSP evolutionMagnetic dipole spin-down (n=3)
with P0 = 1 ms; B = 108G; modified Urca
Internal temperature
Chemicalimbalances
Stationary state
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Insensitivity to initial temperature
Fernández & R. 2005
For a given NS model, MSP temperatures can be predicted uniquely from the measured spin-down rate.
7/8thermal )( L
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The nearest MSP: PSR J0437-4715HST-STIS far-UV observation (1150-1700 Å)
Kargaltsev, Pavlov, & Romani 2004
TR2onconstraint
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PSR J0437-4715: Predictions vs. observation
Fernández & R. 2005
Observational constraints
Theoretical models
2001) al.et Straten (van
18.058.1 SunMM Direct Urca
Modified Urca
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Old, classical pulsars: sensitivity to initial rotation rate
G105.2 11B
Fernández & R., in preparation
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dG/dt ?• Dirac (1937): constants of nature may depend on
cosmological time.• Extensions to GR (Brans & Dicke 1961) supported
by string theory • Present cosmology: excellent fits, dark mysteries,
speculations: “Brane worlds”, curled-up extra dimensions, effective gravitational constant
• Observational claims for variations of– (Webb et al. 2001) – (Reinhold et al. 2006)
See how NSs constrain d/dt of
ce 2EMα
ep mm
cGm 2nGα
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Previous constraints on dG/dtMethod G'/G [yr^(-1)] Timespan[yr] Reference
Solar System planet and 1E-12 24 Williams satellite orbits et al (1996)
Binary pulsar orbit 5E-12 10 Kaspi et al (1994)
Rotation of isolated PSRs 6E-11 10 Goldman (1990)(var. moment of inertia)
White dwarf oscillations 3E-10 20 Benvenuto etal. (2004)
Paleontology: 2E-11 4E+09 Eichendorf &Earth's surface temp. Reinhardt (1977)vs. prehistoric fauna
Binary pulsar masses 2E-12 2E+09 Thorsett (1996)(Chandrasekhar mass attime of formation)
Helioseismology 2E-12 5E+09 Guenther et (Solar evolution models) al. (1998)
Globular clusters 7E-12 1E+10 Degl'Innocenti (isochrones vs. age of the et al. (1996)Universe)
CMB temperature 1E-13 1E+10 Nagata fluctuations (WMAP et al. (2004)vs. specific models)
Big Bang Nucleosynthesis 2E-13 1E+10 Copi(abundances of D, He, Li) et al. (2004)
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Gravitochemical heating
dG/dt (increasing/decreasing gravity) density increase/decrease chemical imbalance non-equilibrium reactions internal heating possibly detectable thermal emission
Paula Jofré, undergraduate thesis Jofré, Reisenegger, & Fernández, paper in preparation
),( epn
0, epn
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-110 yr102/|| GG
PSR J0437-4715Kargaltsev et al. 2004 obs.
Most general constraintfrom PSR J0437-4715
“Modified Urca”reactions (slow )
“Direct Urca”reactions (fast)
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-112 yr104/|| GG
PSR J0437-4715Kargaltsev et al. 2004 obs.
Constraint from PSR J0437-4715assuming only modified Urca is allowed
Slow
Fast
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Constraint from PSR J0437-4715:
...if only modified Urca processes are allowed, and the star has reached its stationary state.
Required time:
Compare to age estimates:
112 yr104/ GG
Myr 90eqt
Gyr 3.55.2
Gyr 9.4
cooling WD
down-spin
t
t
(Hansen & Phinney 1998)
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Now:
Method G'/G [yr^(-1)] Time [yr] Reference
Solar System planet and 1E-12 24 Williams satellite orbits et al (1996)
Binary pulsar orbit 5E-12 10 Kaspi et al (1994)
Rotation of isolated PSRs 6E-11 10 Goldman (1990)(var. moment of inertia)
White dwarf oscillations 3E-10 20 Benvenuto etal. (2004)
Gravitochemical heating 2E-10 1E+05 Jofré et al.of NSs (PSR J0437-4715) (to be published)
MOST GENERAL
Gravitochemical heating 4E-12 9E+07 Jofré et al.of NSs (PSR J0437-4715) (to be published)
ONLY MODIFIED URCA
Paleontology: 2E-11 4E+09 Eichendorf &Earth's surface temp. Reinhardt (1977)vs. prehistoric fauna
Binary pulsar masses 2E-12 2E+09 Thorsett (1996)(Chandrasekhar mass attime of formation)
Helioseismology 2E-12 5E+09 Guenther et (Solar evolution models) al. (1998)
Globular clusters 7E-12 1E+10 Degl'Innocenti (isochrones vs. age of the et al. (1996)Universe)
CMB temperature 1E-13 1E+10 Nagata fluctuations (WMAP et al. (2004)vs. specific models)
Big Bang Nucleosynthesis 2E-13 1E+10 Copi(abundances of D, He, Li) et al. (2004)
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Main uncertainties
• Atmospheric model: – Deviations from blackbody
• H atmosphere underpredicts Rayleigh-Jeans tail
• Neutrino emission mechanism/rate: – Slow (mod. Urca) vs. fast (direct Urca, others)– Cooper pairing (superfluidity)
Not important (because stationary state):
• Heat capacity: steady state• Heat transport through crust
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Conclusions• Rotochemical heating must occur in all neutron stars with
decreasing rotation rates
• Gravitochemical heating happens if dG/dt 0
• Both lead to a stationary state of nearly constant temperature that can be probed with old enough pulsars (e.g., MSPs)
• Observed UV emission of PSR J0437-4715 may be due to rotochemical heating
• The same emission can be used to constrain |dG/dt|:
– competitive with best existing constraints if fast cooling processes could be ruled out
• Sensitive UV observations of other nearby, old neutron stars of different rotation rates are useful to constrain both mechanisms
• Superfluid effects remain to be calculated
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• Pulsar needs to have reached quasi-equilibrium: large age
• Rotochemical effect weaker than gravitochemical: small
Lower right of pulsar P-dP/dt diagram
Also: close enough to measure or constrain thermal emission
Conditions for a good constraint on dG/dt
)2/( PPts
3/|| PP
red) blue,(
yr10,10/|| -11312 GG